a) Preexisting magnetic fields are able to produce anisotropic density
inhomogeneities in the photon fluid and local metric perturbations. In
particular, they are able to produce filamentary structures in the
distribution of the energy density.

b) Particularly interesting are those filaments larger than about
10 Mpc, because they have no problems with magnetic
diffusion (as
mentioned above), because their evolution is more predictable and
because they can be observed today. In fact these radiative and
gravitational potential filaments were the sites where baryons, or any
other dark matter component, collapsed at Recombination, forming the
illuminated supercluster filaments that are observed today as elements
of the
large scale structure. Non linear effects have very much distorted the
pre-Recombination structures, as well as the larger ones, though to a
much lesser extent, as
/ remains low. Therefore, these
pre-Recombination radiative filaments should be identifiable today.

c) The orders of magnitude of these magnetic fields are equivalent to
present
B0 10-8 - 10-9G. If they were much
lower, they
would have no influence on the larger scale structure. If they were much
higher, the
formation of the galaxy would have taken place much earlier.

d) The filament network, if magnetic in origin, must be subject to
some magnetic restrictions. The simplest lattice matching these
restrictions is an "egg-carton" network, formed by octahedra
joining at their vertexes. This "egg-carton" universe would have
larger amounts of matter along the edges of the octahedra, which would
be the sites of the superclusters. Outside the filaments there would be
large voids, devoid not only of baryons but also of magnetic
fields (Fig. 21). Magnetic field lines would be
concentrated in
the filaments, with their directions being coincident with those of the
filaments.

Figure 21. Ideal scheme of the egg-carton
universe formed with
octohedra only contacting at their vertexes. Adopted from
Battaner and Florido (1997).
Courtesy of Astronomy and Astrophysics.

These theoretical speculations are compatible with present
observations of the large scale structure as delineated by the
distribution of superclusters. It is easy to identify at least four of
these giant octahedra in real data, which comprise observational support
for the egg-carton universe. Two of them, those which are closest and
therefore most unambiguously identified, are reproduced in
Fig. 22. Nearly all the important superclusters
in the catalogue by
Einasto et al (1997),
as well as nearly all the important voids in the catalogue by
Einasto et al. (1994)
can be located within the octahedron
structure. This web is slightly distorted by the presence of the very
massive Piscis-Cetus supercluster in one of the filaments.

Figure 22. The two large octahedra closer
to the Milky Way.

The magnetic origin of structures at very large scales alleviates the
old problem encountered by CDM models which predict too little
structure at large scales (see, for instance, the reviews by
Bertschinger, 1998
and Ostriker, 1993).

A fractal nature could be compatible with the octahedron web, in
agreement with the identification of fractals by
Lindner et al. (1996)
from the observational point of view. There could be sub-octahedra
within octahedra, at least in a limited range of length scales. The
simplest possibility is reproduced in
Fig. 23 in which 7 small
octahedra contacting at their vertexes have their egg-carton structure
within a large octahedron, the ratio of large/small
octahedron size being equal to 3. The fractal dimension becomes quantified,
with 1.77 and 2 being the most plausible values. The scale of the fractal
structure would range from 150 Mpc, i.e. slightly lower than the
deepest surveys, down to about 10 Mpc (in agreement with Lindner et
al), as shorter scale magnetic fields would have been destroyed
by the resistive radiation dominated universe. Whether the fractal
egg-carton structure continues indefinitely for larger scales as
suggested by
Sylos Labini et al. (1998)
and others, remains an open question, but
Battaner (1998)
proposed this structure under the adoption of the
Homogeneity Cosmological Principle at large enough scales.

Figure 23. Ideal scheme of the fractal
geometry of the
octahedron network. In this figure we plot the case of a fractal
dimension equal to 1.77. A value of 2 is also an interesting
possibility. Adopted from
Battaner (1998).
Courtesy of Astronomy and Astrophysics.

The absence of a relation between Faraday rotation and redshift of
quasars indicates that a widespread cosmological aligned magnetic field
must be
B0 < 10-11G
(Lesch and Chiba, 1997;
Kronberg, 1994;
Rees and Reinhardt, 1972;
Kronberg and Simard-Normandin,
1976;
Vallée, 1983,
1990).
However, the distribution of large scale magnetic fields
is probably very far from homogeneous. Not only < > = 0, but < B2 >, even if
not vanishing, is far from homogeneous. Instead, we are interested in
the peak values to be found in the matter filaments, in which case
this limit should be increased by a large
factor, even if it is very low in voids, i.e. in the largest
fraction of the volume of the Universe.